There was no show-boating from Jose Mourinho's ruthlessly efficient side and there were a few jitters as they held on to Eden Hazard's goal scored just before halftime.
Victory moved Chelsea to 83 points from 35 games, 13 points clear of Manchester City who hid the disappointment of handing over their title by winning 1-0 at sixth-placed Tottenham Hotspur in Sunday's late kickoff.
Sergio Aguero's 22nd league goal of the season in that game ended a run of four consecutive away defeats for Manuel Pellegrini's side.
City are three clear of Arsenal in the race for runners-up spot with the Gunners, who have five games to play, at relegation battlers Hull City on Monday.
Chelsea's fifth single-goal victory margin in their last seven league games sparked raucous scenes around the ground and on the pitch, with ever-present skipper John Terry leading the celebrations with veteran striker Didier Drogba.
"I am very happy and proud. I need a rest, I'm tired. It's not easy to cope with that, but finally mathematically we are champions now," said a calm and measured Mourinho, who won back-to-back titles in 2004-05 and 05-06.
"Finally we can breathe, relax and enjoy. We can look back and see how much we deserve to be champions."
With blue ticker-tape raining down in the sunshine, Chelsea's players completed a lap of honour with ironic chants of "boring, boring Chelsea" ringing out.
"It's an unbelievable feeling," Terry, who sunk to his knees on hearing the final whistle, told Sky Sports. "We've worked so hard, so to get over the line is great.
"This is what I live for. It's been five years since we've won it. The first one was special and you go four or five years without it and that hurts. So I'll really enjoy it today."
CELEBRATORY MOOD
Blustery, grey conditions had lingered for much of Sunday morning but kickoff in west London was greeted by the sudden emergence of sunshine which reflected the celebratory mood.
A midweek 3-1 victory at Leicester City meant three points against Palace would be enough for Chelsea to become English champions for the fifth time, but Alan Pardew's Palace side were in no mood to play the role of bystanders.
Pardew had won four of his previous six matches as an opposition coach against Chelsea and from the opening stages it was evident his mid-table side had designs on postponing the Blues' title celebrations.
Chelsea were almost gifted a fortuitous lead in the 22nd minute when Palace keeper Julian Speroni punched wildly at Cesc Fabregas's free kick but Nemanja Matic, afforded the freedom of the penalty area, dithered and his shot was diverted wide.
Terry was then lucky to escape conceding a penalty when he appeared to block Jason Puncheon's drive with his arm.
With halftime looming, talisman Hazard had been relatively anonymous by his own standards but he burst into life to draw a challenge from James McArthur and win a penalty.
His spot kick was awful, straight at Speroni, but the ball bounced up invitingly and the Belgian guided a header home.
The second half was a stop-start affair. Drogba wasted a great chance to double the lead and Puncheon fired inches wide for Palace who remained a threat on the counter-attack but never really threatened to gatecrash the party.
Chelsea have lost only twice all season in the league, the sort of consistency that Palace manager Alan Pardew recognised made them the benchmark for the rest.
"That's why he (Mourinho) earns the money he does. He wins. He wins trophies and he will win them in any manner he thinks is right for that particular occasion," said Pardew, who got one over the Portuguese this season when still in charge of Newcastle United.
